J Austral Math Soc Ser A 49 pp303--308, 1990.

Riesz Sets and the Radon-Nikodym Property

Patrick N. Dowling

(Received 21 June 1989)

Abstract

Let X be a complex Banach space, G a compact abelian group and L a subset ofÙG, the dual group of G. Then L_L¹(G, X) has the Radon-Nikodym property if and only if X has the Radon-Nikodym property and L is a Riesz set. In aprticular, H¹(T, X) has the Radon-Nikodym property if and only if X has the Radon-Nikodym property. This solves a problem of Hensgen.

1980 AMS Subject Classification (1985 Revision): 46B22, 43A46

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Authors

Patrick N. Dowling: Miami University, Oxford, Ohio 45056, U.S.A.

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Last Modified: Wed Feb 19 10:27:52 2003